Identify the sequence as arithmetic, geometric, or neither. Explain your answer.
1.6, 0.8, 0.4, 0.2, . . .
Thanks for being helpful :3
This sequence is geometric with a common ratio of 1/2. Each term is half of the previous term.
To identify whether the given sequence is arithmetic, geometric, or neither, we need to look for a specific pattern in the sequence.
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. For example, if we have a sequence like 2, 4, 6, 8, 10, the common difference is 2.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. For example, if we have a sequence like 2, 4, 8, 16, 32, the common ratio is 2.
Let's look at the given sequence: 1.6, 0.8, 0.4, 0.2, ...
To determine if it is arithmetic, we would need to find a constant difference between each pair of consecutive terms. However, in this sequence, we don't see any common difference between terms. For instance, 1.6 - 0.8 = 0.8 - 0.4 = 0.4 - 0.2 = 0.4, showing that there is no consistent difference. Therefore, this sequence is not arithmetic.
Now let's consider if it is geometric. For a sequence to be geometric, we need to find a constant ratio between each term and its previous term. Taking any pair of consecutive terms, we can observe that 1.6 ÷ 0.8 = 0.8 ÷ 0.4 = 0.4 ÷ 0.2 = 2. As a result, the common ratio is 2. Hence, this sequence is geometric with a common ratio of 2.
In summary, the given sequence 1.6, 0.8, 0.4, 0.2, ... is geometric since there is a constant ratio of 2 between each term and its previous term.